Meanfield solution of the dissipative transverse Ising model
Abstract
Phase transitions in dissipative quantum systems have been investigated using various analytical approaches, particularly in the meanfield (MF) limit. However, analytical results often depend on specific methodologies. For instance, the Keldysh formalism shows that the dissipative transverse Ising (DTI) model exhibits a discontinuous transition at the upper critical dimension, $d_c= 3$; however, the fluctuationless MF approach shows that a continuous transition occurs in infinite dimensions ($d_\infty$). Thus, analytical results must be confirmed by numerical verification. However, this may not be feasible owing to the exponential increase in computational complexity as $\mathcal{O}(2^{2N})$ with system size $N$. However, if we assume that the spins are fully connected in infinite dimensions ($d_\infty$), the spin indices are permutationsymmetric. This symmetry significantly reduces the complexity, to $\mathcal{O}(N^3)$. Using this symmetry, we simulate the DTI model on fully connected networks with large system sizes. Using finitesize scaling analysis, we show that the upper critical dimension of the DTI model is not $3$ but a noninteger dimension $3.5$; thus, the discontinuous transition that occurs at high dissipation strength is not an MF result, but is induced by fluctuation effects below $d_c$. We conclude that the DTI model with strong dissipation exhibits a continuous transition above $d_c$, as predicted using the fluctuationless MF approach, and we determine the critical exponents.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09435
 Bibcode:
 2021arXiv211009435J
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 11 pages, 9 figures